Polar Star Quantitative Commodity Fund

Dr Mauritz van den Worm, PhD

06 December, 2018

Manual vs Automated Trading

How has the increase of Automated Trading Systems (ATS) influenced the futures market?

  • CME transaction data identitifies ATS with the 1028 tag
  • Data available from November 2012 to present
  • Consider data form 2012 to 2016
  • Use gradient plots to highlight the changes
  • Graphs are interactive

MAN vs ATS - Group

MAN vs ATS - Agriculture

MAN vs ATS - Energy

Trade Participation

Where are the opportunities?

  • Limited, Local, Spectrum
    • Less liquid parts of the curve
    • Changes to macro
    • Concentrated risk on asymmetric risk/reward trades


  • Quantitative
    • Harvest systematic risk premium from large universe of commodities
    • Rule based decision making process
    • Strategies inspired by discretional methodology

Literature

Grinold’s Fundamental Law of Active Portfolio Management

Law of active portfolio management

\[ \text{Performance} = \text{Skill} \times \sqrt{\text{Breadth}} \]

Suppose we are in a coin flipping casino

  • Flip coins in stead of futures
  • The coin is biased - \(P(\text{heads}) = 0.51\)

How does the betting work?

  • We have 1000 coins
  • The minimum wager is 1 coin
  • If you win you gain 1 coin
  • If you loose you loose 1 coin
  • There are 1000 tables with coin wagers
  • Games runs in parallel

What is the optimal way to allocate coins?

Two extremes

  • Bet 1000 coins on one coin flip
  • Bet 1 coin on 1000 coin flips

Expected Return

  • Single bet: \(0.51 \times 1000 + 0.49 \times (-1000) = 20\)

  • Multi bet: \(1000 \times [0.51 + 0.49 \times (-1)] = 20\)

The same expected return

Risk - Probability to lose it all:

  • Single bet: 49%

  • Multi bet: \(0.49 \times 0.49 \times \dots \times 0.49 = 0.49^{1000} \approx 0\)

Risk - Standard Deviation:

  • One coin per table

\[ \text{risk} := \text{std}\left\{1,-1,-1,1, \dots, 1 \right\} = 1 \]

  • One 1000 coin bet, 999 zero coin bets

\[ \begin{align} \text{risk} &:= \text{std}\left\{1000,0,0,0, \dots, 0 \right\} = 31.62 \\ \text{risk} &:= \text{std}\left\{-1000,0,0,0, \dots, 0 \right\} = 31.62 \end{align} \]

Coin Flip Casino - Reward/Risk

  • Just like Sharpe Ratio

  • Single bet: \(\text{SR}_{\text{single}} = \frac{20}{31.62} =0.63\)

  • Multi bet: \(\text{SR}_{\text{multiple}} = \frac{20}{1} =20\)

Coin flipping casino - Observation

  • \(20 = 0.63 \times \sqrt{1000}\)

  • \(\text{SR}_{\text{multiple}} = \text{SR}_{\text{single}} \times \sqrt{\text{Bets}}\)

  • \(\text{Performance} = \text{Skill} \times \sqrt{\text{Breadth}}\)

How does this apply to commodity futures?

  • We use insights gained from years of fundamental trading to inspire bespoke quantitative strategies that are applied to a large collection of commodity markets

  • We increase breadth or diversification by
    • how,
    • what and
    • when we trade

Literature

Technical considerations when trading futures systematically

  • Continuous Futures Price Series
    • We require long time series data
    • Futures expire too soon to gather sufficient data
    • How do you handle rolls?


  • Non-stationarity of Price Data
    • Time series data can only reliably be forecasted if stationary
    • Machine Learning algorithms are designed for stationary features
    • How do we create stationary data?

Continuous Futures Price Series

Continuous Futures Curves

Stationarity

Stationarity

How to obtain a stationary time series


  • Traditional
    • Price differences
    • Returns
    • Memory loss


  • Modern
    • Fractional differences
    • Memory present

Stationarity

Stationarity

Infrastructure

Core Strategies - Carry

Carry overview

  • Take advantage of curve shape
  • Contango is typically less steep in further dated contracts, i.e. it has a lower roll yield than near dated contracts
  • Extract roll yield with a short position in the near and a long position in the far dated contracts of the same commodity

Carry Example

Carry Example

Flavours of carry

  • Carry - inspired by discretionary methodology (BB1)
    • 30 commodities and 2 tenors
    • Sizing determined using percentile methodology
    • Risk 0.5% of strategy NAV per trade
    • Monthly rebalance


  • Machine Learning Enhanced Carry (BB2)
    • 30 commodities and 2 tenors
    • Fractionally differenced time-series
    • Meta labelling
    • Ensemble machine learning
    • Deterine probability of profitable trade and size trade accordingly

Backtest Assumptions

  • $10 Round trip of each contract
  • Slippage of 1 tick per contract


  • Entry cost of one spread \(= \text{\$}10 + 2 \text{ ticks} \times \text{multiplier}\)
  • Exit cost of one spread \(= \text{\$}10 + 2 \text{ ticks} \times \text{multiplier}\)

BB1 - Statistics

BB1 - Statistics

BB1 - Statistics

BB2 - Statistics

BB2 - Statistics

BB2 - Statistics

Systematic Carry - Statistics

Statistic BB1 BB2
Annualized Return 5.480 19.210
Annualized Sharpe (Rf=0%) 0.662 1.239
Annualized Std Dev 8.270 15.500
Average Negative Month Return -1.572 -2.821
Average Positive Month Return 1.933 4.380
Maximum Drawdown 26.683 39.529
Maximum Drawdown/Annualized Return 4.869 2.058
Number of Negative Months 103.000 95.000
Number of Positive Months 147.000 154.000

Carry literature

Literature on extracting carry from futures:

Literature on applying machine learing techniques in algorithmic trading:

Core Strategies - Trend

Trend overview

  • Trend following is about absolute performance of each commodity
  • Identify trends over selection of time frames
  • Slowly build position as trend increases
  • Slowly exit position as trend decreases
  • 35 Commodities and 2 tenors

Trend - Statistics

Trend - Statistics

Trend - Statistics

Trend - Statistics

Statistic TR1
Annualized Return 18.930
Annualized Std Dev 17.800
Annualized Sharpe (Rf=0%) 1.064
Maximum Drawdown 26.683
Maximum Drawdown/Annualized Return 1.410
Number of Positive Months 142.000
Number of Negative Months 107.000
Average Positive Month Return 5.710
Average Negative Month Return -3.497

Trend literature

Core Strategies - Relative Roll

Relative Roll overview

Strategy not yet live.

Relative Roll literature

Core Strategies - Sentiment

Sentiment overview

Strategy not yet live.

Sentiment literature

Quantitative Portfolio

Investment Thesis

  • Focus on the intersection of technolody, data and behavioral finance applied to the broad commodity space
  • Build strategies based on sound economic theory to help deliver long-term repeatable results. Inspired by
    • academic and
    • proprietary research.
  • Investment process built on the scientific method consisting of the systematic
    • observation,
    • measurement,
    • experiment,
    • hypothesis formulation,
    • testing and
    • modification of hypothesis

Quantitative Portfolio - Statistics

Quantitative Portfolio - Statistics

Quantitative Portfolio - Statistics

Quantitative Portfolio - Statistics

Quantitative Portfolio - Statistics

Statistic 1998- 2008- 2015-
Annualized Return 19.930 18.960 5.900
Annualized Sharpe (Rf=0%) 1.701 1.644 0.634
Annualized Std Dev 11.720 11.530 9.310
Average Negative Month Return -2.107 -2.258 -2.304
Average Positive Month Return 4.055 4.156 2.835
Maximum Drawdown 18.722 13.709 12.802
Maximum Drawdown/Annualized Return 0.939 0.723 2.170
Number of Negative Months 100.000 54.000 23.000
Number of Positive Months 156.000 83.000 30.000

Quantitative Portfolio as supplement to S&P500

Portfolio Comparison

Statistic S&P500 PSQCF PSQCF and S&P500
Annualized Return 5.410 18.610 11.230
Annualized Sharpe (Rf=0%) 0.368 1.255 1.028
Annualized Std Dev 14.710 14.830 10.920
Average Positive Month Return 3.069 3.988 2.796
Avereage Negative Month Return -3.583 -2.097 -2.019
Number of Negative Months 95.000 101.000 96.000
Number of Positive Months 154.000 148.000 153.000
Worst Drawdown 52.556 19.692 32.728

Polar Star Multi Strategy Portfolio

Polar Star Products and S&P500

Combine Discretionary and Systematic Portfolios

Polar Star Multi Strategy as enhancement to S&P500

Portfolio Comparison

Statistic S&P500 PS Multi Strategy PS Multi Strategy and S&P500
Annualized Return 12.890 15.410 14.470
Annualized Sharpe (Rf=0%) 1.139 1.524 1.931
Annualized Std Dev 11.320 10.110 7.490
Average Positive Month Return 2.794 2.860 2.151
Avereage Negative Month Return -2.385 -1.705 -1.389
Number of Negative Months 32.000 34.000 27.000
Number of Positive Months 64.000 62.000 69.000
Worst Drawdown 17.028 6.905 7.038

Summary

Combining a

  • discretionary and
  • systematic approach

to investing in commodities we create a product with

  • positive expected return which is
  • uncorrelated to equities

that gives superior risk adjusted returns.